Random Destructive Acts via Focused Solar Radiation

Updated 2003.03.19
slashdotted 2004.05.21
This is a copy of the original page at http://www-personal.umich.edu/~bclee/lens.html
The University of Michigan will be deleting all www-personal web pages in 2012.

Jacob Dickinson informed me that Alltronics.com sells a rectangular
lens similar in size to the infamous lens we had, and a few weeks ago
I got one (see below). It's thinner than the Edmund's lens we used to
have and needed a frame, but it's big and about half the price of
Edmund's lens. You can find it at http://www.alltronics.com/lenses.htm
and it was $99 plus shipping when I looked.

If you're looking for something smaller and a lot cheaper, you can
often find cheap surplus (used) 12" Fresnel lenses at American Science and Surplus and Scientifics (the new
owner of the Edmund Scientific Catalog) for as little as $3.

And to answer another only slightly less frequently asked question, no
the beloved Dershem Memorial Lens is not for sale. We decided
it would go to the first of us to get a Ph.D. (in other words, to
first order we left it up to fate) and Chris Chaput was the proud
winner. Thus Dr. Chris now owns the lens and (for obvious reasons) it
is kept at least 1000 miles away from him at all times.

People also ask, "What was the area of the focus?" The best we
ever got was about a centimeter across. The lens was somewhat
flexible so the corners didn't tend to contribute much. A professor
at U of M who had one of these said he built a frame with cross
supports and was able to get more of the lens to contribute to the
focus.

A lot of people want to know what temperatures we achieved.
It's hard to make this estimate, the real question should be how much
power the lens can supply (and you can see more about this below).
But in terms of estimates, we certainly melted aluminum which has a
melting point of 660.37 degC. We never quite managed to melt copper
with the old lens but (melting point of 1083.4 degC) but we have with
the new one (see below) so I think we could have if the sidewalk had
not been so fragile. Assuming a black body target and that the sun
supplies 1340 W/m^2 (before atmospheric absorption) we calculated that
we should be able to melt quartz (1610 degC) but in practice I don't
believe we achieved temperatures that high.

The target was (certainly past tense) a zinc penny. The copper turned
into a black crust and the zinc ran out the side (that silver blob
going up in these pictures). The target stage was some shale like
rock we had sitting around, which would flake when heated but didn't
pop and eject the target.

We have since taken many targets and caused them to
melt/incinerate/explode (it's a pain to clean pop off the lens) and
soon I will add a few more pictures.

Impressive as destroying a penny may seem, I estimated that we may
have only managed to get maybe 10 percent of the available
energy hitting the lens (roughly 1kW) into the penny:

Mass of a zinc penny: 0.0025 kg

Specific heat of zinc: 390 J/kgK

Melting point of zinc: 419.58 degC

Thus 20degC to about 420degC takes 390 J

Latent heat of fusion for zinc: 1.1x10e5 J/kg

Thus to melt the penny takes about 275 J

We heated the liquid zinc considerably as well, but I will ignore that.

Total energy in the penny: > 665 J

It takes something under or around 6 seconds to melt a penny:

665 J / 6 sec gives us a lower limit of about >= 111 Watts

Sunlight at the earth: 1365 W/m^2

Transmission of the earth's atmosphere: maybe 65-70% at this angle with some clouds?

Area of the lens is about 1.1m^2

Power on the lens: approx. 1000 W

Power to the penny >= 10.0%

This is likely at least a slight underestimate of the lens' output for
at least a couple reasons: it was slightly cloudy and the sun was not
all that high (effective transmission may have been much lower);
likely a lot of the energy went into the stage instead of the target
(the metal stage we used later was pretty badly warped when we were
done). We hope to improve on this by making stands and will try to
measure it more carefully. This is optically a better lens than the
old Edmunds one (better image) and as Edmunds points out, optically
better Fresnel lenses tend to be less efficient light concentrators,
so maybe that's part of our problem too -- there was a nice central
focus (smaller than the penny) but a lot of the light was scattered
into a much larger area, at least a foot across. This may make the
lens more useful for diffuse heat applications (cooking) than
concentrated ones. We'll see . . .

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